Geometry

We know that the value of a cylinder is πr²h, where r and h are the radius and height respectively. So, we know that 2π(r +6)² – 2πr² = y = πr² (2 + 6) – 2πr².

Expanding and rearranging, we get that 2π(12r +36) = 6πr².

Divide both sides by 6π to get that 4r + 12 = r^2, and rearrange to see that r² – 4r – 12 = 0. This factors to become (r-6) (r + 2) = 0. So, r = 6 or r = -2.

Obviously, the radius cannot be negative, so our answer is 6.